By means of the Rabinowitsch equation (Rabinowitsch, 1929; Oldroyd, 1956), one can derive a plot of momentum flux (say T

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By Means Of The Rabinowitsch Equation Rabinowitsch 1929 Oldroyd 1956 One Can Derive A Plot Of Momentum Flux Say T 1 (49.07 KiB) Viewed 26 times

By means of the Rabinowitsch equation (Rabinowitsch, 1929; Oldroyd, 1956), one can derive a plot of momentum flux (say T) versus velocity gradient (say - dv/dr) for any fluid from experimental data on pressure drop versus flow rate for laminar, isothermal flow through circular tubes. The only assumptions that need to be made are that the fluid is homogeneous throughout and that the fluid does not slip at the tube wall. (a). Show that the integral for the volume rate of flow may be integrated by parts to give Q=-T dv. Jo dr (b). Introduce the change of variable r/R=T/T (where T = (P.-P₁)R/2L is the momentum flux at the wall, r=R), and rewrite the integral in (a) in terms of the integration variable T (c). Differentiate the integral in (b) with respect to r to obtain the Rabinowitsch equation dv. = 1 d TRT dTR - (TO) dr r=R Explain how this equation can be used to obtain the T versus (-dv, / dr) curve desired.